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a). Assign the keys, 59, 140, 30, 41,68, 115, 70, 155, 99, 92 to the nodes of the binary search tree shown below. Feel free to do trials and errors to fill the tree with the given list of keys. b). There are a list of random keys and a binary search tree. The tree shape is fixed like the example below and you can't change it. The number of keys in the list is the same as the number of available nodes of the tree. We want to systematically fill in all the nodes of the tree with the randomly ordered list of the keys. Describe an algorithm to fill the tree completely. c). Starting from the root node, we want to populate a BST with the keys from a given list without altering its order. Using the keys and the tree in question a) as an example, show the ordered list of the keys which can be sequentially inserted into the tree. Also, explain and demonstrate how you would get such a list systematically using the tree from question b). Please limit your description to a sentence or two. d). Describe why this specific instance of binary search tree below can't be colored to form a valid red-black tree even without populating keys. e). Now let's try to do two rotations to make it an RB tree. Describe how rotations are done and show the final picture of an RB tree showing each node with a key value and its color.

a). Assign the keys, 59, 140, 30, 41,68, 115, 70, 155, 99, 92 to the nodes of the binary search tree shown below. Feel free to do trials and errors to fill the tree with the given list of keys. b). There are a list of random keys and a binary search tree. The tree shape is fixed like the example below and you can't change it. The number of keys in the list is the same as the number of available nodes of the tree. We want to systematically fill in all the nodes of the tree with the randomly ordered list of the keys. Describe an algorithm to fill the tree completely. c). Starting from the root node, we want to populate a BST with the keys from a given list without altering its order. Using the keys and the tree in question a) as an example, show the ordered list of the keys which can be sequentially inserted into the tree. Also, explain and demonstrate how you would get such a list systematically using the tree from question b). Please limit your description to a sentence or two. d). Describe why this specific instance of binary search tree below can't be colored to form a valid red-black tree even without populating keys. e). Now let's try to do two rotations to make it an RB tree. Describe how rotations are done and show the final picture of an RB tree showing each node with a key value and its color.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Q1) Answer the following questions in a separate document. a). Assign the keys, 59, 140, 30, 41,68, 115, 70, 155, 99, 92 to the nodes of the binary search tree shown below. Feel free to do trials and errors to fill the tree with the given list of keys. b). There are a list of random keys and a binary search tree. The tree shape is fixed like the example below and you can't change it. The number of keys in the list is the same as the number of available nodes of the tree. We want to systematically fill in all the nodes of the tree with the randomly ordered list of the keys. Describe an algorithm to fill the tree completely. c). Starting from the root node, we want to populate a BST with the keys from a given list without altering its order. Using the keys and the tree in question a) as an example, show the ordered list of the keys which can be sequentially inserted into the tree. Also, explain and demonstrate how you would get such a list systematically using the tree from question b). Please limit your description to a sentence or two. d). Describe why this specific instance of binary search tree below can't be colored to form a valid red-black tree even without populating keys. e). Now let's try to do two rotations to make it an RB tree. Describe how rotations are done and show the final picture of an RB tree showing each node with a key value and its color.
Transcribed Image Text:Q1) Answer the following questions in a separate document. a). Assign the keys, 59, 140, 30, 41,68, 115, 70, 155, 99, 92 to the nodes of the binary search tree shown below. Feel free to do trials and errors to fill the tree with the given list of keys. b). There are a list of random keys and a binary search tree. The tree shape is fixed like the example below and you can't change it. The number of keys in the list is the same as the number of available nodes of the tree. We want to systematically fill in all the nodes of the tree with the randomly ordered list of the keys. Describe an algorithm to fill the tree completely. c). Starting from the root node, we want to populate a BST with the keys from a given list without altering its order. Using the keys and the tree in question a) as an example, show the ordered list of the keys which can be sequentially inserted into the tree. Also, explain and demonstrate how you would get such a list systematically using the tree from question b). Please limit your description to a sentence or two. d). Describe why this specific instance of binary search tree below can't be colored to form a valid red-black tree even without populating keys. e). Now let's try to do two rotations to make it an RB tree. Describe how rotations are done and show the final picture of an RB tree showing each node with a key value and its color.
ERST PR Tree ond Dynemie Dregromming (LCS)
Transcribed Image Text:ERST PR Tree ond Dynemie Dregromming (LCS)
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